pahade: people from hilly region
Madhesi: from terai region
here is the story that my grandpa told me, in short:
Long ago, the people living in terai region used to speak.."rajbansi, tharu, maithili" languages, and most of them were indian decent. none of them could speak nepali (they cannot speak nepali fluently till now). the population was very low, just few of such people were residing in the terai region.
on the other hand, only those who were living in hills could speak nepali, fear of malayria at that time made them reluctant to move to terai. after the eradication of malayria, people from hilly region started flocking in terai, the reasons were basically easy farming, and easy life.
so the ppl who moved from hills later called pahade...